Euler Number Fluid Calculator

Calculate Euler number from pressure difference, density, and characteristic velocity.

Eu = Δp / (ρv²)

Pressure difference Δp (Pa)

Density ρ (kg/m³)

Velocity v (m/s)

Enter valid values in all required fields.

What this formula means

Euler number compares pressure forces with inertial forces. It appears in similarity analysis for pumps, turbines, valves, nozzles, and other flows where a pressure change accompanies a characteristic velocity.

Use Euler number in turbomachinery scaling, pressure-drop comparisons, wind-tunnel similarity, and nondimensional flow analysis. The result should be interpreted with consistent units and with the assumptions of the underlying model in mind.

Worked example

For Δp = 50 kPa, ρ = 1000 kg/m³, and v = 5 m/s, Eu = 2.

Applications

Use Euler number in turbomachinery scaling, pressure-drop comparisons, wind-tunnel similarity, and nondimensional flow analysis. It is also useful as an independent check when comparing hand calculations, laboratory measurements, simulations, or preliminary engineering estimates.

Assumptions and common mistakes

Important: Some references use a factor of one-half in the denominator and call the result a pressure coefficient. Confirm the convention before comparing values.

Use SI units unless the field label states otherwise. Keep significant figures appropriate to the accuracy of the inputs, and do not treat a simplified calculator as a replacement for codes, detailed design standards, or professional review.

Frequently asked questions

What equation does this calculator use?Eu = Δp / (ρv²). The calculator evaluates the displayed relationship using the values entered above.

Are the results unit-sensitive?Yes. The input labels use SI units so the displayed output follows the corresponding SI unit.

Can I use this for engineering design?Use it for learning and preliminary checks. Final designs require validated data, applicable standards, safety factors, and professional judgment.